aYOLD DIFFUSION IN THE DYNAMICS OF A 4-MACHINE POWER SYSTEM UNDERGOING A LARGE

We f o c u s on the seemingly complicated dynamics of a four-machine power system which i s undergoing a sudden fau l t . Adopt ing a Hamil tonian (energy) formu l a t i o n , we c o n s i d e r t h e s y s t e m a s a n i n t e r c o n n e c t i o n of (one degree of reedom) subsystems. Under cer ta in c o n f i g u r a t i o n ( a s ta r ne tk-ork)and parameter va lues we e s t a b l i s h t h e p r e s e n c e o f A r n o l d d i f f u s i o n w h i c h e n t a i l s p e r i o d i c , a l m o s t p e r i o d i c , a n d c o m p l i c a t e d nonperiodic dyanmics a l l s i m u l t a n e o u s l y p r e s e n t ; a n d e r r a t i c t r a n s f e r o f e n e r g i e s b e t w e e n t h e s u b s y s t e m s . I n s e c t i o n 1 we i n t r o d u c e t h e t r a n s i e n t s t a b i l i t y p r o b l e m i n a ma themat i ca l s e t t i ng and exp la in wha t ou r r e s u l t s mean i n t h e power sys tems contex t . Sec t ion 2 p r o v i d e s i n s i g h t s i n t o A r n o l d d i f f u s i o n a n d s u m m a r i z e s i t s m a t h e m a t i c a l f o r m u l a t i o n a s i n [ 8 ] , [ l ] . S e c t i o n 3 g i v e s c o n d i t i o n s f o r w h i c h A r n o l d d i f f u s i o n a r i s e s on c e r t a i n e n e r g y l e v e l s o f t h e s w i n g e q u a t i o n s . These cond i t ions are v e r i f i e d a n a l y t i c a l l y i n t h e c a s e when a l l b u t one subsystem (machine) undergo re lat i v e l y small o s c i l l a t i o n s .